Semi-analytical Modeling of the Influence of Macro Bending Effects on Micro Contact-Inhomogeneity Problems

This study examines the effects of macroscopic bending and microscopic contact loading in inhomogeneous materials using a semi-analytical model based on Eshelby’s equivalent inclusion method.The model accounts for bending effects through the beam theory,with bending stress included in the Eshelby’s equivalent inclusion equations.The macroscopic displacement resulting from bending effects is incorporated into the microscopic contact solver,and the final displacement is determined using the conjugate gradient method in an iterative solution.Computational efficiency can be improved by incorporating the discrete convolution and fast Fourier transform.The core scheme is validated using the finite element method,yielding accurate and efficient results for bending-contact problems in inhomogeneous materials.Simulations reveal the interplay between bending,contact loading,and inhomogeneity,as stress around the inhomogeneity alters and the stress concentration area expands under increasing bending moments.Conversely,low-magnitude negative bending moments reduce both contact pressure and stress around the inhomogeneity.The position where inhomogeneities are least affected shifts from the neutral surface depending on the coupling effect.The model provides a valuable bridge for connecting the macroscopic bending effect and microscale contact-inhomogeneity problems by visualizing stress fields and assessing pressure distributions.

NUMERICAL-PERTURBATION ANALYSIS OF EDGE EFFECT IN BENDING LAMINATED PLATE

In this paper, we consider a bending laminated plate. At first, the dimensionless variables are used to transform the equilibrium equations of any layer to perturbation differential equations. Secondly, the composite expansion is used and the solution domain is divided into interior and boundary layer regions and the mathematical models for the outer solution and the inner solution are yielded respectively. Then, the inner solution is expressed with the boundary intergral equation.

Performance evaluation of ultra-long lithium heat pipe using an improved lumped parameter model

Lithium heat pipes have broad applications in heat pipe cooling reactors and hypersonic vehicles owing to their ultra-high working temperature.In particular,when the length of the lithium heat pipe is ultra-long,the flow and heat transfer characteristics are more complex.In this study,an improved lumped parameter model that considers the Marangoni effect,bending effect,and different vapor flow patterns and Mach numbers was developed.Thereafter,the proposed model was verified using the University of New Mexico’s Heat Pipe and HTPIPE models.Finally,the verified model was applied to simulate the steady-state operation of an ultra-long lithium heat pipe in a Heat PipeSegmented Thermoelectric Module Converters space reactor.Based on the results:(1)Vapor thermal resistance was dominant at low heating power and decreased with increasing heating power.The vapor flow inside the heat pipe developed from the laminar to the turbulent phase,whereas the liquid phase in the heat pipe was always laminar.(2)The vapor pressure drop caused by bending was approximately 22–23%of the total,and the bending effect on the liquid pressure drop could be ignored.(3)The Marangoni effect reduced the capillary limit by hindering the liquid reflux,especially at low vapor temperatures.Without considering the Marangoni effect,the capillary limit of the lithium heat pipe was overestimated by 9%when the vapor temperature was 1400 K.(4)The total thermal resistance of the heat pipe significantly increased with increasing adiabatic length when the vapor temperature was low.Further,the wick dryness increased with increasing adiabatic length at any vapor temperature.Such findings improve on current knowledge for the optimal design and safety analysis of a heat pipe reactor,which adopts ultra-long lithium heat pipes.

Studies on the key parameters in segmental lining design

The uniform ring model and the shell-spring model for segmental lining design are reviewed in thisarticle. The former is the most promising means to reflect the real behavior of segmental lining, while thelatter is the most popular means in practice due to its simplicity. To understand the relationship and thedifference between these two models, both of them are applied to the engineering practice of FuzhouMetro Line I, where the key parameters used in both models are described and compared. The effectiveratio of bending rigidity h reflecting the relative stiffness between segmental lining and surroundingground and the transfer ratio of bending moment x reflecting the relative stiffness between segment andjoint, which are two key parameters used in the uniform ring model, are especially emphasized. Thereasonable values for these two key parameters are calibrated by comparing the bending momentscalculated from both two models. Through case studies, it is concluded that the effective ratio of bendingrigidity h increases significantly with good soil properties, increases slightly with increasing overburden,and decreases slightly with increasing water head. Meanwhile, the transfer ratio of bending moment xseems to only relate to the properties of segmental lining itself and has a minor relation with the groundconditions. These results could facilitate the design practice for Fuzhou Metro Line I, and could alsoprovide some references to other projects with respect to similar scenarios.

On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory:equilibrium,governing equation and static deflection

This paper has successfully addressed three critical but overlooked issues in nonlocal elastic stress field theory for nanobeams： （i） why does the presence of increasing nonlocal effects induce reduced nanostructural stiffness in many, but not consistently for all, cases of study, i.e., increasing static deflection, decreasing natural frequency and decreasing buckling load, although physical intuition according to the nonlocal elasticity field theory first established by Eringen tells otherwise？ （ii） the intriguing conclusion that nanoscale effects are missing in the solutions in many exemplary cases of study, e.g., bending deflection of a cantilever nanobeam with a point load at its tip; and （iii） the non-existence of additional higher-order boundary conditions for a higher-order governing differential equation. Applying the nonlocal elasticity field theory in nanomechanics and an exact variational principal approach, we derive the new equilibrium conditions, do- main governing differential equation and boundary conditions for bending of nanobeams. These equations and conditions involve essential higher-order differential terms which are opposite in sign with respect to the previously studies in the statics and dynamics of nonlocal nano-structures. The difference in higher-order terms results in reverse trends of nanoscale effects with respect to the conclusion of this paper. Effectively, this paper reports new equilibrium conditions, governing differential equation and boundary condi- tions and the true basic static responses for bending of nanobeams. It is also concluded that the widely accepted equilibrium conditions of nonlocal nanostructures are in fact not in equilibrium, but they can be made perfect should the nonlocal bending moment be replaced by an effective nonlocal bending moment. These conclusions are substantiated, in a general sense, by other approaches in nanostructural models such as strain gradient theory, modified couple stress models and experiments.